Question

you let a pendulum go and watch it swing back and forth. at what point of the swing does the potential energy of the pendulum equal its total energy? ignore any outside forces that would slow the pendulum. (1 point)
just after it reaches the other side and begins swinging down
at the bottom of the swing
halfway from the top of the swing to the bottom
at the top of the swing

Explanation:

The total mechanical energy of a pendulum is the sum of its kinetic energy ($KE=\frac{1}{2}mv^{2}$) and potential energy ($PE = mgh$). At the top of the swing, the pendulum's velocity \(v = 0\), so \(KE=0\). The total energy \(E=KE + PE\). When \(KE = 0\), \(E=PE\).

• Just after it reaches the other side and begins swinging down: At this point, the pendulum has both kinetic and potential energy.
• At the bottom of the swing: Here, the height \(h\) is minimum (assuming \(h = 0\) at the bottom in a common - reference frame), so \(PE\) is minimum and \(KE\) is maximum.
• Halfway from the top of the swing to the bottom: At this position, the pendulum has both kinetic and potential energy.

Answer:

at the top of the swing